Using Grammars to Generate Very Large Scale Neighborhoods for the Traveling Salesman Problem and Other Sequencing Problems

Local search heuristics are among the most popular approaches to solve hard optimization problems. Among them, Very Large Scale Neighborhood Search techniques present a good balance between the quality of local optima and the time to search a neighborhood. We develop a language to generate exponentially large neighborhoods for sequencing problems using grammars. We develop efficient generic dynamic programming solvers that determine the optimal neighbor in a neighborhood generated by a grammar for sequencing problems such as the Traveling Salesman Problem or the Linear Ordering Problem. This framework unifies a variety of previous results on exponentially large neighborhood for the Traveling Salesman Problem and generalizes them to other sequencing problems.

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